Results 1 to 2 of 2

Math Help - Inequalities problem

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    17

    Inequalities problem

    Question: Let a and b be the roots of the quadratic equation x^2- (m +\frac 3 m )x +2 = 0 where m is a non-zero constant.
    Using the fact that (a-b)^2 \geq  0 for all real numbers a and b, show that m^2 +\frac 9 {m}^2 \geq 6.
    Hence show tha t (m + \frac 3 m }^2 \geq 12

    MY WORK:
     (a-b)^2 = (a+b)^2 - 4ab = (a+b)^2 - 8 \geq 0
     (m+ \frac 3 m ) -8 \geq 0
     m^2+6m+\frac 9 {m}^2 \geq 8

    Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2008
    Posts
    588
    Thanks
    87
    Quote Originally Posted by cakeboby View Post
    Question: Let a and b be the roots of the quadratic equation x^2- (m +\frac 3 m )x +2 = 0 where m is a non-zero constant.
    Using the fact that (a-b)^2 \geq  0 for all real numbers a and b, show that m^2 +\frac 9 {m}^2 \geq 6.
    Hence show tha t (m + \frac 3 m }^2 \geq 12

    MY WORK:
     (a-b)^2 = (a+b)^2 - 4ab = (a+b)^2 - 8 \geq 0
     (m+ \frac 3 m ) -8 \geq 0
     m^2+6m+\frac 9 {m}^2 \geq 8

    Thanks in advance.
    From your first line of working onwards, you'll actually want to use

     (m + \frac{9}{m})^2 - 4(m)(\frac{3}{m})  \geq 0

     m^2 + 6 + (\frac{9}{m})^2 - 12 \geq 0

     m^2 +  (\frac{9}{m})^2  \geq 6

    Check the binomial expansion. You did this incorrectly in your working.
    Last edited by Gusbob; August 17th 2010 at 07:37 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Inequalities Problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 11th 2011, 03:49 AM
  2. inequalities problem help!
    Posted in the Algebra Forum
    Replies: 7
    Last Post: February 1st 2010, 03:10 AM
  3. inequalities problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 5th 2008, 01:59 PM
  4. Inequalities Problem..
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 12th 2007, 09:51 PM
  5. Problem with inequalities
    Posted in the Algebra Forum
    Replies: 1
    Last Post: July 19th 2007, 04:37 AM

Search Tags


/mathhelpforum @mathhelpforum